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Video Transcript

TranscriptSolving Systems of Equations by Graphing

Red Riding Hood and the Wolf are both walking through the forest. To figure out if and where they will meet we can solve a system of equations by graphing.

Let's look at a map of the forest. Red Riding Hood starts here and is walking in this direction. The Wolf starts here and is walking in this direction. It looks like they will meet at some point, but lets take a closer look using math.

When you look at the map, you can see that it looks like a cartesian coordinate system.

Red Riding Hood's path is along the line 2y - 4 = x. The Wolf's path is along the line y = 2x - 10. As you can see, the equation for the Wolf's path is already in slope-intercept form, so we can graph it easily. Let's transform the equation of Red Riding Hood into slope-intercept form as well.

Transforming Equations into Slope-Intercept Form

Slope-intercept form is y = mx + b. The first step in transforming this equation into slope-intercept form is to add 4 to both sides. Now you have 2y = x + 4. It is almost in slope-intercept form.

You just need to move the 2 in front of the y. You can do this by dividing by 2 on both sides. This reduces to y = 1/2 x + 2. Now the equation is in slope-intercept form.

Solving Equations by Graphing

Let's graph the lines. Red Riding Hood's equation is y = 1/2 x + 2. This means that the slope is 1/2 and the y-intercept is at (0, 2).

First, let's plot the y-intercept (0, 2). Now, because the slope represents rise over run, you can count up 1 and right 2 to plot the next point. You can keep counting up one and right two to plot more points.

The Wolf's equation is y = 2x - 10. This means that the slope is 2 and the y-intercept is at (0, -10). Since (0, -10) isn't visible on the graph let's plot our first point somewhere else.

The wolf looks close to where x = 5. When you plug in 5 for x the y-value is 0. Now you can plot the point (5, 0). Since the slope is 2 you can plot more points by moving up 2 and right one.

The two paths intersect at the point (8, 6). Whether or not Red Riding Hood and the Wolf will meet depends on how fast or slow they are both walking.

Imagine the Wolf's path could be described by y = x/2 + 3. Will they meet? Let's draw the graph.

The y-intercept is at (0, 3). Then we plot more points by counting up one and right two. The two lines are now parallel to each other so they will never intersect.

Now imagine the Wolf walked along the line y = 2x/4 + 4/2. Where will they meet? Let's draw the graph. The y-intercept is at (0, 2). To plot more points we count up 2 and right 4. As you can see the graphs are the same, which means there are infinitely many possible meeting points.

Let's get back to our first scenario. Red Riding Hood and the Wolf are walking toward the intersection point. Red Riding Hood sees the Wolf and is shocked for a split second. Phew, it's only Jim heading to the same Halloween Party. So they decide to walk together.

About this Video Lesson

Description

A system of equation is two or more equations with the same variables. To determine the point where the equations meet, the solution to the system, there are several methods: graphing, substitution, and elimination.

This video investigates how to use graphs to solve systems of equations. To determine where lines will meet on the coordinate plane (coordinate grid), manipulate each equation in the system, so it is written in slope-intercept form, y = mx + b. You can do this by isolating the y-value or the vertical coordinate.

Now using information from the equations written in slope-intercept form, you can graph the lines. Remember b is the y-intercept, and m is the slope or the rise over the run. First, mark the y-intercept, then using the slope value, you can mark a couple other points on the line and last connect the dots to draw a line. Do this for every equation in the system. The point where the lines intersect is the solution to the system and also the ordered pair that will satisfy all the equations in the solution.

How can a system of equations be useful in the real world? Well imagine you want to accidentally bump into someone, if you knew the equation of their path and the equation of your path… To learn more about this topic, watch the video.